"Five Al-Qaeda members" were killed in the southern Shabwa province when clashes broke out after militants ambushed a military convoy, a security official said.
One soldier was killed and five others were wounded in the gunfight east of the town of Ataq, the official said.
Earlier the defence ministry said on its 26sep.Net news website that army forces killed "two Saudi terrorists, Ibrahim Hamad and Ahmed al-Harbi," in the town of Azzan, also in Shabwa.
The provinces of Abyan and Shabwa and the neighbouring central province of Baida have been the focus of the offensive.
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President Abdrabuh Mansur Hadi vowed Thursday to clear Al-Qaeda from all its remaining bastions by extending the offensive to other regions.
He named Marib, east of Sanaa, where Al-Qaeda is firmly implanted.
A military official cited by state news agency Saba today said "Al-Qaeda members are still being hunted" and stressed that the operation "will continue until they are cleared."
The jihadists' Yemen franchise, Al-Qaeda in the Arabian Peninsula, took advantage of a 2011 uprising that forced veteran president Ali Abdullah Saleh from power to seize large swathes of the south and east.
The army recaptured several major towns in 2012 but has struggled to reassert control in rural areas despite recruiting militia allies among the local tribes.